Pavlov M. On the classification of homogeneous differential-geometric third-order Poisson brackets, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)
Speaker: Maxim Pavlov
Title: On the classification of homogeneous differential-geometric third-order Poisson brackets
Abstract:
Homogeneous differential-geometric Poisson brackets were introduced by Dubrovin and Novikov in 1984. Such operators appear in many integrable systems. First order operators have been extensively studied so far. In this talk we will devote ourselves to the classification of third order operators. Starting from old results by one of us (GVP) we will give a complete description of third-order operators for a number of components not greater than 3, and a description of third-order operators for a number of components equal to 4 in a generic case that could be fruitfully extended to a higher number of components. Joint work with G.V. Potemin and R. Vitolo.